Permutation Complexity of the Thue-Morse Word
Combinatorics
2010-04-06 v2
Abstract
Given a countable set X (usually taken to be the natural numbers or the integers), an infinite permutation \pi of X is a linear ordering of X. This paper investigates the combinatorial complexity of the infinite permutation on the natural numbers associated with the well-known and well-studied Thue-Morse word. A formula for the complexity is established by studying patterns in subpermutations and the action of the Thue-Morse morphism on the subpermutations.
Cite
@article{arxiv.1003.6123,
title = {Permutation Complexity of the Thue-Morse Word},
author = {Steven Widmer},
journal= {arXiv preprint arXiv:1003.6123},
year = {2010}
}